Make a cardboard template of the seat and back (do this before making the chair, its easier).
Cut a strip of wadding and using PVA glue, stick all the pieces onto it face down. When the glue is dry, trim around each piece.
Cut a piece of fabric about 1/2 inch wider all round. Cut the corners.
Using your glue, stick two sides first, then fold corners in before sticking the rest down. (You will probably find you get lovely sticky fingers doing this step.) Try to keep it taught, but not so tight that it flattens the batting.
When you turn it over, it should look nicely padded like this.
Once that's complete you may wish to trim the sides of the seat with narrow braid as I have done.